The NBUTA Class of Life Distributions

by A.N. Ahmed, Emad Shokry.

Abstract:
A new class of life distributions, namely new better than used in the total time on test on average transform ordering (TTTA), is introduced. The relationship of this class to other classes of life distributions, and closure properties under some reliability operations, are discussed. We provide a simple argument based on stochastic orders that the class is closed under the formation of series systems in case of independent identically distributed components. Behavior of this class is developed in terms of the monotonicity of the residual life of k -out-of n systems given the time at which the (n-k)-th failure has occurred.
Finally, we discuss testing exponentially against the aging property.